OFFSET
1,1
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
Paul Erdős and Norbert Hegyvári, On prime-additive numbers, Studia Scientiarum Mathematicarum Hungarica, Vol. 27, No. 1-2 (1992), pp. 207-212. Review.
EXAMPLE
30 = 2 * 3 * 5 = 2 + 3 + 5^2.
42 = 2 * 3 * 7 = 2^3 + 3^3 + 7 = 2^5 + 3 + 7.
MATHEMATICA
primes[n_] := First[Transpose[FactorInteger[n]]]; maxPower[p_, n_] := Module[{k=0, nn=n}, While[nn>1, nn/=p; k++]; k-1]; a[n_] := Module[ {ps=primes[n]}, np=Length[ps]; pws=Table[maxPower[ps[[k]], n], {k, 1, np}]; npws=Length[pws]; Coefficient[Product[Sum[x^(ps[[k]]^j), {j, 1, pws[[k]]}], {k, 1, np}], x, n]]; s={}; Do[b=a[n]; If[b>0, AppendTo[s, n]], {n, 1, 2100}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 12 2018
STATUS
approved